Can you solve the impossible day of the week logic puzzle?

Can you solve for the day of the week Abby was born? What about Barry? This is an incredible logic riddle.

van Ditmarsch, Hans, Michael Ian Hartley, Barteld Kooi, Jonathan Welton, and Joseph BW Yeo. "Cheryl's Birthday." arXiv preprint arXiv:1708.02654 (2017).

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[Tehom]

A "perfect logicians" puzzle always makes me think that at the end it's going to be "Sorry, no, that's wrong, the other person messed up a couple of turns back"

[markotrieste]

Three logicians go into a bar.
The bartender asks, "Do you all want a beer?"
The first logician says, "I don't know."
The second logician says, "I don't know."
And the third logician says, "Yes."

[mihailghinea]

The post of mohitrawat5225 reminds me of a joke...

A mathematician, a physicist, and an engineer are riding a train through Scotland.

The engineer looks out the window, sees a black sheep, and exclaims, "Hey! They've got black sheep in Scotland!"

The physicist looks out the window and corrects the engineer, "Strictly speaking, all we know is that there's at least one black sheep in Scotland."

The mathematician looks out the window and corrects the physicist, " Strictly speaking, all we know is that there is at least one sheep with at least one black side in Scotland."

[paalvaa]

I had a different strategy... I noticed that everything is symmetric around Monday, in that any logic that can eliminate e.g. Tuesday must necessarily also eliminate Sunday, and so on. The only day that doesn't get eliminated in a pair is Monday itself, so if you can end up with exactly one day Abby could be born on, it must be Monday, regardless of what kind of logic the two actually used to get there. For the same reason it can't be possible to determine which day adjacent to Monday Barry was born on.

[teambellavsteamalice]

Perhaps it's easier to deduce if you order the combos differently, like in a circle.
So Sunday/Monday, Monday/Tuesday, Tuesday/Wednesday, etc.

This way you can go along the circle, eliminating options. As you eliminate in both directions you end up at the other side of the circle with the Monday/Sunday and Monday/Tuesday options.

[kaizoisevil]

Funny thing is that after Barry says yes, Abby would still say no, because she still cannot conclude whether Barry was born on Sunday or Tuesday.

[Jonathan_Welton]

Well, that was a pleasant surprise. The accreditation was unexpected and very gracious of you. Thank you Presh.

[DidWeWin]

I think this is a lot easier to grasp visually, with a radial arrangement.

Mon
b

Sun Tue
1a 1a



Sat 2b 5a 5a 2b Wed



4b 4b
3a 3a
Fri Th



Notation:
a = Abby known to NOT be born on indicated day
b = Barry known to NOT be born on indicated day
preceding number = the number of "no" responses, i.e. the step

[spacemario]

Solved it mentally, and dude, it's insanely hard to keep track of my thought

[mohitrawat]

Once a mathematician, a biologist, a physicist and a chemist were sitting together in a coffee shop. They saw 2 people going in a house and after some time 3 people came from the same house. The biologist said " There must be reproduction happened in the house". The physicist said " There must be a wormhole inside the house". The chemist said " The house must had a nuclear fission reaction in it". The mathematician then said " If one more person will enter the house, the house would be empty". Now the question is who among them was right?

[dannieee]

I love these types of puzzles so much!! I'm running a math club and I always like to propose these puzzles on the members, thank you so much, please do more of these :D!

[justinnitoi]

Write out all the days of the week in circle. M for monday, T for tuesday, ... Su for sunday.
Now we define !B to mean Barry cannot be born on that day and !A for Abby.
Notice that we start with !B on M.

Every turn, when Abby says No, that tells barry that she cannot be adjacent to any days with a !B (for otherwise, she would know it must be the other day). Thus, on any turn where she says no, add a !A to any days adjacent to the !B days.
The same is done with adding a !B to any days adjacent to !A days when Barry says no.

So after doing this process, all the days end up having a !A on them except Monday.
also, all the days end up having a !B on them except Sunday and tuesday.
Therefore, Abby must be born on Monday and Barry can be born on Tuesday or Sunday.

Note that this method can be generalized quite neatly if you want to consider a number of cycle days more than 7.

[johnmcho]

Abigail Grundy, born on a Monday, christened on Tuesday, and married on Wednesday. On Thursday, she fell sick, and the illness got worse on Friday, and she died on Saturday.

[perceivecreativity]

Finally, I managed to solve one of these tricky logic puzzles correctly before watching the solution. Took a while.

[tuckertechnolord]

I sent the entire video distracted by whatever’s going on with barry’s ankle

[kyogre]

This is the first one of your riddles I solved as I was hearing the beginning part of it! I am getting better at these logician puzzles

[kevinhull]

I used check marks next to the days of the week under two columns: one for Abby and one for Barry. I paused after your pairs to check and got the same result, and also to see if I could figure out the day Barry was born on.

[SaIamander]

figured abby was born on monday cuz why the heck else would barry not be born on that day :/

[chachachi-hhks]

I used square "days of week" by "days of week" grid. Then I started putting X in each cell where combination of days of week could NOT happen. It allowed me easily solve the puzzle

[Pilot-guxz]

I love logic puzzles like this, you can solve them in your head and train your memory and logical thinking.